High-fidelity analysis of multilayered shells with cut-outs via the discontinuous Galerkin method

Abstract

A novel numerical method for the analysis of multilayered shells with cut-outs is presented. In the proposed approach, the shell geometry is represented via either analytical functions or NURBS parametrizations, while generally-shaped cut-outs are defined implicitly within the shell modelling domain via a level set function. The multilayered shell problem is addressed via the Equivalent-Single-Layer approach whereby high-order polynomial functions are employed to approximate the covariant components of the displacement field throughout the shell thickness. The shell governing equations are then derived from the Principle of Virtual Displacements of three-dimensional elasticity and solved via an Interior Penalty discontinuous Galerkin method over a discretization of the shell modelling domain that is obtained by intersecting a background structured grid with the level set function defining the cut-outs. To maintain high-order accuracy even in proximity of the embedded cut-outs, high-order accurate quadrature rules for implicitly-defined regions are employed to compute the integrals of the method while a cell-merging technique avoids the presence of overly small cut cells. The combined use of these features represents the novelty of the proposed method and provides a high-fidelity approach to the analysis of multilayered shells with cut-outs. Numerical tests are performed to model the static response of a cylindrical shell and a NURBS-based shell with a cut-out. The obtained results are compared with those obtained using the Finite Element method and show the accuracy and the computational efficiency of method.